Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have a set of data that looks like this:

Person 1 [48 total records]
2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 1,
--
Person 2 [56 total records]
1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1,
--
Person 3 [18 total records]
1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1,

A '1' indicates a false answer, and a '2' indicates a correct one. I want to be able to compare records to see if any people in the data set are performing significantly above or below average. I've heard of using z-scores and standard deviation, but I'm not sure if that's the correct approach, or even how I would go about doing the calculation.

I also need to find out the minimum number of records I would need in order to have sufficient confidence in the results.

My math skills are pretty limited, so a simple explanation would be greatly appreciated.

share|improve this question
    
It's easy to find scores that are above and below average, but where to draw the boundary between significant and not significant is a personal opinion. Would you mind clarifying what is significant for your purposes? –  Matt Calhoun Aug 16 '12 at 2:16
    
I thought significance was a technical term that indicates whether the product indicates a pattern, rather than just chance. Or am I confusing it with confidence levels? –  Jeremy Aug 16 '12 at 5:29
add comment

1 Answer

How about a very simple solution that can give you kind of an overview?

  1. for each person, calculate the percentage of correct answers (= the number of 2's / total records).
  2. group these numbers into groups, e.g. 0-10%, 10-20%, .... Count the numbers in each group. This gives you an overview of how people perform, e.g. 6/10 people belongs to the 80-90% group and 4/10 in the 20-30%.
share|improve this answer
    
This approach is more reasonable, but many journals in a wide swatch of sciences - particularly biomedicine and healthcare, sociology &c, favor pre-WW2 methods that involve "significance." Stanford statistician Efron in his new book "Large Scale Inference" wrote in a footnote that he no longer refers to patterns as "significant" but rather as "interesting" –  alancalvitti Aug 15 '12 at 23:31
    
Is there a reason why the "significance" approach is a problem? I thought significance was a technical term that indicates whether the product indicates a pattern, rather than just chance. –  Jeremy Aug 16 '12 at 5:31
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.